Indian Journal of Geo-Marine Sciences ol. 4(8), December 013, pp. 1049-1056 Evaluation of submarine model test in towing tank and comparison with CD and experimental formulas for fully submerged resistance Mohammad Moonesun 1, Mehran Javadi, * Pejman Charmdooz 3 & Karol Uri Mikhailovich 4 1 National University of Shipbuilding Admiral Makarov (NUS), aculty of Ship Design, Isfahan University of echnology (iut), Isfahan, Iran Aero-Maritime Science & Research Center, Isfahan University of echnology (iut), Isfahan, Iran 3 Department of Marine Science & Engineering, Malek-Ashtar University of echnology (MU), Isfahan, Iran 4 National University of Shipbuilding Admiral Makarov (NUS), aculty of Ship Design, Malek-Ashtar University of echnology (MU), Isfahan, Iran * [E-mail: p.charmdooz@yahoo.com] Received 5 December 01; revised 13 September 013 owing tanks experiments were conducted to study the behavior of flow on a model of underwater vehicle with tango shape of nose. Length of model and prototype vehicle is 1 and 3 meters, respectively. irst the method of underwater model test is evaluated by unequal Reynolds number. An accurate method has been suggested for scaling of results between model and main submarine in underwater testing. Suitable depth for ignoring the free surface effects has been suggested. After underwater test in towing tank and extracting the results, the CD results have been compared. At last, for more validation of results, four groups of experimental formula for submarine bare hull resistance in deep water have been presented. inally, the comparison tables and diagrams show the accuracy of each of these six methods in the calculation of submerged resistance of submarine and present an optimum resistance coefficient for this submarine. [Keywords: Submarine, Resistance, ully submerged, Model test, CD, Experimental result] Introduction he most ideal shape for the submerged mode is shown in ig. 1. In this case, the pressure resistance is only 10 percent of the total resistance showing an efficient body. Other form is parallel middle body (igure 1) that is more similar to the actual shape of submarines that is easier to construction. ully submerged mode is a situation of underwater movement without any effects on the surface i.e. free surface of water can be ignored. or this reason, the shapes of the submarine and aircraft are similar because of absence of free surface effects. Ship moves in the interference of water and air with free surface effects (surface mode) and therefore a sharp stem of bow is suitable. Main different between submerged and surfaced mode is wave making and wave breaking resistance. ully submerged modes have only viscous pressure resistance (form resistance) and frictional resistance. ariation of frictional and form resistance with L/D variation is shown in ig. & 3. By increasing L/D, frictional resistance increases and form resistance decreases. hen, the effects of L/D on two items of resistance are paradoxical; thus, there is a unique optimum resistance that total resistance is minimum. otal resistance diagram is shown in ig. 3. Lowest point of diagram is related to the optimum L/D. ig. 1 Suitable orm for Submarine Hull ig. Schematic of the overall test set-up
1050 INDIAN J. MAR. SCI., OL. 4, NO. 8 DECEMBER 013 or teardrop shape, (ideal shape) the optimum L/D is 6 and in parallel middle body form, the optimum L/D is 10. In naval submarines, the approximate resistance of main hull and appendages are shown in able 1. Appendage resistance is 35 percent of total resistance [1]. Materials and Methods Experiments were conducted in Isfahan University of echnology (IU) marine laboratory. owing tank has 108 length, 3 width and. depth. Basin is equipped with a trolley that is able to operate in through 0.05-6 m/s speed that moves by two 7.5 KW electromotors with ±0.0 m/s accuracy. System is prepared with a proper frequency encoder, i.e., 500 pulses in a minute, which decreases the uncertainty of measurements. Dynamometer was calibrated by calibration weights []. A three degree of freedom dynamometer is used for force measurements. Data are recorded via an accurate data acquisition system. Dynamometer is equipped with 100 N load cells. An amplifier set is used to raise signals of load cells and to reduce the noise sensitivity of the system. he experiment is conducted with a submarine model that is made by wood ig. 3 ariation of Submarine Resistance by L/D Ratio according to IC recommendations [3]. ango nose submarine is a type of submarine that has been tested in undersurface motion. All data are filtered to eliminate the undesirable acceleration, primary and terminative motion of trolley. rolley was controlled in wireless system from control room of lab. Data presented in this paper for each point are an average of several towing tank runs [4]. or each run, at least 750 samples in 15 seconds were collected and the ensemble averaged. Schematic of the model and the overall test set-up are shown in igure. Dimensions of studied submarine in this paper are shown in able with parallel middle body form. Relation L/D is equal to 8.88 because of limitation of design and internal arrangements. Hull bow is elliptical and stern is conical. Main submarine has a deck with 8 meters of length, 0.4 meters of height and 1 meter of beam. Also, it has a conning tower of 3. meters length and 3 meters of height on top of the main hull. Maximum submerged speed is 14 knots and wetted surface area is 450 square meters. All dimensions of this submarine have been scaled by 1:3. ully Submerged Standard Condition Wave making procedure is in the interference of air and water produced by variation of fluid pressure. When a submarine goes from surface to submerge mode, wave making decreases until fully omitted 1. ig. 4 shows that the resistance coefficient (C D ) decreases by increasing submergence depth. In this diagram, h is submerged depth, L is submarine length, and D is submarine diameter. Standard depth for fully submerged condition is different in several references. In reference 5 this depth is half of submarine length (h=l/), in reference 6 depth is 3D (h=3d), and in reference [7] depth is 5D (h=5d). Our experiment shows that h=5d is the best option but there is no difference between the results. Before full submergence of submarine, there are some ripples on the water surface, which are omitted after full submergence of body (ig. 5). able 1 Percentage of Appendages in Submarine Resistance Main body Bridge fin Stern planes Bow planes Upper rudder Lower rudder Sonar fairing keel otal(%) 65.5 7.67 7.61 3.44 5.4 1.71.78 6.05 100 Overall length Hull diameter able Main Submarine Dimensions (meter) Displacement (t) Bow length Cylinder length Conical stern length Conical stern Angle (deg) 3 3.6 35 5 1 6 16.7
MOONESUM et al.: EALUAION O SUBMARINE MODEL ES IN OWING ANK 1051 ig. 6 ariation of iscous Resistance vs Reynolds Number ig. 4 otal Resistance Coefficient vs Depth ig. 5 Wave Making Coefficient vs roude Number and Depth of Submergence Method of Developing Result of Model to Main Submarine at Submerged est At submerged mode, roude equation cannot be used because of absence of free surface effects and waves. Also, the use of Reynolds equation is impossible because model speed will be too large and impossible to provide. ( Re) = ( Re) M S ( ) =. LS / L M S M or this submarine with a speed of 14 knots (7. m/s) and scale of 1:3, the speed of model will be 3 times of main submarine, which is equal to 30 m/s that is actually impossible. Main aid of Reynolds equation is independent from turbulent current on model surface. his turbulence ig. 7 ariation of rictional Resistance vs Reynolds Number can be provided with several methods such as making roughness of submarine s bow. hus, we can be sure that the currents on both model and main submarine are turbulent. In the depth of water, there are only frictional and viscous pressure resistances and there is not a wave resistance. ariation of frictional resistance coefficient and viscous pressure resistance coefficient curve after critical Reynolds (turbulent current) at rough zone is straight horizontal, and shows constant coefficient. Schematic curve of variation is shown in igures 6, 7. As mentioned before, in beneath stages, model results can be developed to main submarine 8 : Making roughness of model s bow and confidence of turbulent flow on the model body Calculation of model total resistance ( R ) M Calculation of total resistance coefficient ( C ) M Calculation of frictional resistance coefficient ( C ) M by IC-1957 method Calculation of viscous pressure coefficient: ( C ) ( C ) ( C ) P = M M Equalizing viscous pressure coefficients of model and submarine: ( ) ( ) ( ) (( ) ) C P = C P = M C P S
105 INDIAN J. MAR. SCI., OL. 4, NO. 8 DECEMBER 013 Calculation of frictional resistance coefficient of submarine by IC-1957 at actual Reynolds of submarine Calculation of total resistance coefficient: ( C ) S = ( C ) S + ( C ) P Calculation of total resistance of submarine: R 1... = C A D ρ he above-mentioned stages can provide a very good estimation for developing the results of model to submarine. Methods of Resistance Calculation of ully Submerged Submarine or calculation of submarine resistance in fully submerged condition, there are some experimental based formula with rather accurate results and small errors. hese methods with model test method and CD method can provide a suitable estimation of resistance. hese results are not exactly equal and similar. By omission of diverged results, the final estimation can be exact and correct. Method 1) this method is for the calculation of bare hull resistance by several diagrams in Reference 1 C = C + C + C P A In this method resistance coefficient can be extracted from these diagrams. Results of calculations by method 1 are in able 4. Method ) his method is mentioned in Reference [9]. Conditions of use for this method are: L D Length to diameter ratio: 5 7 Depth of submergence more than 5 times of diameter: h 5D After these conditions, bare hull resistance can be calculated as follows: 1- Calculation of frictional resistance coefficient by IC-1957 -Added resistance from surface roughness equal to 5 percent of C: δc = 0.05 C C = C o f + δc 3-Calculation of form coefficient (K): D D K = + 1.5 L L 3 4-iscous pressure coefficient by: C = C = K. C P orm o 5-otal resistance coefficient: C = C + C P 6-Calculation of total resistance of bare hull: 1 R = C. ρ. A. where A is wetted surface area. Appendage resistance must be added to the above. Results of calculation by method are shown in able 5. 0.075 C = 0 log Re able 4 Results of Method 1 ( ) Method 3) his method is in Reference 10 by these stages for bare hull resistance: 1-rictional resistance coefficient by IC-1957 (knot) (m/s) Re (C ) S C R C A C (KN) 1 0.514 14964364 0.008 0.0007 0.0004 0.0039 0.38 1.09 99877 0.005 0.0007 0.0004 0.0036 0.881 3 1.543 44893091 0.003 0.0007 0.0004 0.0035 1.897 4.058 59857455 0.00 0.0007 0.0004 0.0034 3.75 5.57 7481818 0.00 0.0007 0.0004 0.0033 5.005 6 3.086 8978618 0.001 0.0007 0.0004 0.003 7.081 7 3.601 104750545 0.001 0.0007 0.0004 0.003 9.498 8 4.115 119714909 0.000 0.0007 0.0004 0.0031 1.5 9 4.630 13467973 0.000 0.0007 0.0004 0.0031 15.340 10 5.144 149643636 0.000 0.0007 0.0004 0.0031 18.758 11 5.658 164608000 0.0019 0.0007 0.0004 0.0031.505 1 6.173 17957364 0.0019 0.0007 0.0004 0.0030 6.578 13 6.687 19453677 0.0019 0.0007 0.0004 0.0030 30.974 14 7.0 09501091 0.0019 0.0007 0.0004 0.0030 35.69
MOONESUM et al.: EALUAION O SUBMARINE MODEL ES IN OWING ANK 1053 able 5 Results of Method (knot) (m/s) Re C 0 C C k C orm C (KN) 1 0.514 14964364 0.008 0.0001 0.009 0.1146 0.0003 0.0033 0.199 1.09 99877 0.005 0.0001 0.006 0.1146 0.0003 0.009 0.710 3 1.543 44893091 0.003 0.0001 0.005 0.1146 0.0003 0.007 1.500 4.058 59857455 0.00 0.0001 0.004 0.1146 0.0003 0.006.553 5.57 7481818 0.00 0.0001 0.003 0.1146 0.000 0.005 3.858 6 3.086 8978618 0.001 0.0001 0.00 0.1146 0.000 0.005 5.409 7 3.601 104750545 0.001 0.0001 0.00 0.1146 0.000 0.004 7.00 8 4.115 119714909 0.000 0.0001 0.001 0.1146 0.000 0.004 9.5 9 4.630 13467973 0.000 0.0001 0.001 0.1146 0.000 0.003 11.48 10 5.144 149643636 0.000 0.0001 0.001 0.1146 0.000 0.003 13.965 11 5.658 164608000 0.0019 0.0001 0.000 0.1146 0.000 0.003 16.674 1 6.173 17957364 0.0019 0.0001 0.000 0.1146 0.000 0.00 19.604 13 6.687 19453677 0.0019 0.0001 0.000 0.1146 0.000 0.00.754 -otal frictional resistance coefficient: 1.5 3 D D C + = C 1+ 1.5 7 L L 3-Calculation of total bare hull resistance: R = 1 C. ρ. A. where A is wetted surface area. Appendage resistance must be added to this amount. Results of calculations by method 3 are in able 6. Method 4) this method is also in Reference 10. his method is similar to method 3 with a different way for calculating C his coefficient is: C = C D D 3 + 4.5 L L 0.5 D + 1 L where S is cross section area of submarine. Results of method 4 are presented in able 7. R = 1 C. ρ. S. Method 5) his method is based on model test 11. or successful experiment of the model, bow part of submarine is made carefully (ig. 8). hese tests are done at fully submerged condition (igure 9). or turbulent current at low speeds, the bow part of the model is roughed. he results of model test in towing tank are presented in able 8. As mentioned before, resistance coefficient variation after critical Reynolds will be constant and rather equal to 0.0039. hus, according to the mentioned stages for developing the results, the resistance of submarine in several speeds is in able 9. (knot) (m/s) able 6 Results of Method 3 Re C 0 C (KN) 1 0.514 14964364 0.0080 0.0099 0.18 1.09 99877 0.0050 0.0067 0.651 3 1.543 44893091 0.0035 0.0050 1.374 4.058 59857455 0.005 0.0040.338 5.57 7481818 0.0017 0.003 3.533 6 3.086 8978618 0.001 0.006 4.954 7 3.601 104750545 0.0007 0.001 6.593 8 4.115 119714909 0.0003 0.0017 8.448 9 4.630 13467973 0.0000 0.0013 10.515 10 5.144 149643636 0.00197 0.0010 1.789 11 5.658 164608000 0.00194 0.0007 15.70 1 6.173 17957364 0.0019 0.0005 17.953 13 6.687 19453677 0.00190 0.000 0.838 14 7.0 09501091 0.00188 0.0000 3.9 (knot) (m/s) able 7 Results of Method 4 Re C 0 C (KN) 1 0.514 14964364 0.0080 0.0059 0.361 1.09 3853336 0.0040 0.00508 1.38 3 1.543 57799855 0.006 0.00477.619 4.058 77066473 0.0016 0.00457 4.460 5.57 96333091 0.0009 0.00443 6.745 6 3.086 1.16E+08 0.0004 0.00431 9.460 7 3.601 1.35E+08 0.0000 0.004 1.597 8 4.115 1.54E+08 0.00196 0.00414 16.146 9 4.630 1.73E+08 0.00193 0.00407 0.101 10 5.144 1.93E+08 0.00190 0.00401 4.456 11 5.658.1E+08 0.00187 0.00396 9.06 1 6.173.31E+08 0.00185 0.00391 34.346 13 6.687.5E+08 0.00183 0.00387 39.87 14 7.0.7E+08 0.00181 0.00383 45.780
1054 INDIAN J. MAR. SCI., OL. 4, NO. 8 DECEMBER 013 ig. 8 Construction of Model and Bow of Submarine ig. 9 Submarine Model est in owing ank (knot) able 8 Results of model test in towing tank (m/s) ( ) M (C ) M =(C ) S.916019 1.5 4.43 0.00384.71617 1.4 3.9 0.003883.5716 1.3 3.4 0.003949.33815 1..96 0.004011.138414 1.1.48 0.003999 1.94401 1.05 0.004 1.749611 0.9 1.68 0.004047 1.5551 0.8 1.37 0.004177 1.360809 0.7 1.08 0.004301 1.166407 0.6 0.76 0.004119 0.97006 0.5 0.55 0.00493 able 9 Model est Results in Speeds 1-14 knots S (knot) S (m/s) ( ) S (KN) 0 0 0.0000 1 0.5144 0.380 1.088 0.950 3 1.543.140 4.0576 3.8080 5.57 5.9499 6 3.0864 8.5679 7 3.6008 11.6619 8 4.115 15.319 9 4.696 19.778 10 5.144 3.7998 11 5.6584 8.7977 1 6.178 34.717 13 6.687 40.16 14 7.016 46.6476 ig. 10 Submarine Simulation in luent Method 6) CD method: o evaluate the hydrodynamic performance of the submarine, CD analyses are utilized and the results are compared with those of the model tests and experimental formula. LUEN, a commercial CD code is one of the efficient codes for CD analyses. otal resistance was estimated and compared with the results of the model tests and experimental ormulas. he simulation in this paper involved solving the incompressible Reynolds Average Navier-Stocks (RANS) equations 1, 13. At first, CAD geometry, as starting point, has been possible to automate the generation and meshing of a suitable computational domain for test on the basis of vehicle geometry. Also, all tests have been performed using an unstructured hexagonal mesh with prism layer adjacent to the underlying solid surface. Because of depending on the region in space surrounding the submarine, the meshes are refined. Additionally, the left and top boundaries of the domain are modeled as velocity inlet, the right boundary was modeled as an outflow boundary, and the surface of the body itself was modeled as a wall (ig. 9). In this work, SS k-ω model is used to simulate turbulent flow past underwater vehicle hull forms 14.
MOONESUM et al.: EALUAION O SUBMARINE MODEL ES IN OWING ANK 1055 his simulation as shown in igure 10 is with hull and appendages. Structured and unstructured grids are used to mesh the domain around hull as shown in igure 10. he results of CD method are shown in able 10. Amount of each part of submarine in total resistance at speed 8 knot is shown in able 11. Results and Discussion Before analyzing these methods, it must be noted that methods 1 to 4 are for bare hull, and methods 5, 6 are for hull and appendages. Appendages resistance is about 35 percent of total resistance. hen, results of methods 1 to 4 must be completed. Comparisons of results are shown in able 1 and ig. 11. able 10 Results of CD Analysis (knot) (KN) 0 0 1 0.63 1.359 3.16 4 3.346 5 4.637 6 6.368 7 8.863 8 1.5553 9 19.4 10 3.55 11 6.98 1 30.567 13 34.54 14 37.386 able 11 otal Resistance in Speed 8 Knot Pressure force (N) 6749.168 iscous force (N) 5804.1003 otal force (N) 1553.631 According to them, except method 1 and 4, results of other methods are rather near and similar with less than 0 percent difference. herefore, the total resistance of 45 KN can be a good estimate for this model. he best way for calculating a submarine resistance is to evaluate the methods such as experimental base formula, CD, & towing tank tests together. Best method that most of the time has acceptable errors is experimental test in towing tank (of course if the test conditions are not applied in a correct way, the unacceptable error will be inevitable) but towing tank test is not always possible or available, so with considering the errors the other methods can be used 15. o show the competence of the methods for such these models, comparison of the other methods with towing tank test results can be extracted from able 1. ig. 11 Resistance-Speed Diagrams for 6 Methods (knot) Method 1 able 1 otal Resistance of Main Submarine (KN) Method Method 3 Method 4 Method 5 Method 6 1 0.36677514 0.30590877 0.801496 0.554917 0.379978 0.63 1.3547646 1.09801 1.000784 1.905195 0.9519911 1.359 3.9187164.3079857.1136407 4.086747.14198.16 4 5.03809373 3.9753338 3.5968143 6.861308 3.8079645 3.346 5 7.69959057 5.93595174 5.4361133 10.376349 5.9499446 4.637 6 10.893471 8.3190174 7.611537 14.55413 8.56790 6.368 7 14.611165 11.0765105 10.14381 19.37956 11.661891 8.863 8 18.8493033 14.19598 1.997444 4.839863 15.31858 1.5553 9 3.599797 17.663858 16.176468 30.94559 19.778 19.4 10 8.8590756 1.485444 19.676073 37.64564 3.799778 3.55 11 34.6304 5.650906 3.49049 44.931916 8.79773 6.98 1 40.8886748 30.1603163 7.60659 5.839551 34.71681 30.567 13 47.65343 35.006596 3.058548 61.34114 40.165 34.54 14 54.9113617 40.1866041 36.8068 70.430891 46.647565 37.386
1056 INDIAN J. MAR. SCI., OL. 4, NO. 8 DECEMBER 013 or reference speed of 1 knots, errors percentages are as follows: Method 1: 19% Method : 11% Method 3: 19% Method 4: 54% Method 6: 10% So, according to these results, in the case of a similar model as described (parallel middle body), and suitable scaling method, various models resistance (model with different diameter, length, length of parallel body and ) can be calculated. References 1 Burcher R, Rydill L J, Concept in submarine design, (he press syndicate of the University of Cambridge., Cambridge university press), 1998, pp. 95. IC (3 th International owing ank Conference), Recommended procedures and guidelines, Sample Work Instructions Calibration of Load Cells, 7.6-0-09, 00. 3 IC (3 th International owing ank Conference), Recommended procedures and guidelines-model Manufacture Ship Models, 7.5-01-01-01, 00. 4 IC (3 th International owing ank Conference), Recommended procedures and guidelines esting and Extrapolation Methods- Resistance Uncertainty Analysis, 7.5-0-0-01, 00. 5 Rawson K J, upper E C, Basic Ship heory, (Jordan Hill., Oxford), 001, pp. 731. 6 Jackson H A, Submarine Design Notes, (Massachusetts Institute of echnology).198, pp. 50. 7 Moonesun M, Handbook of Naval Architecture Engineering, (Kanoon Pajohesh., Isfahan), 009, pp.1003. 8 Lewis Edward, Principles of Naval Architecture, (he Society of Naval Architects and Marine Engineers), 1988, pp. 36. 9 Bertram, Practical Ship Hydrodynamics, (Elsevier Ltd., UK), 000, pp. 369 10 Pulmor. J, Underwater ehicle Design with Regard to Power plant Selection, 001. 11 Mackay M, he Standard Submarine Model: A Survey of Static Hydrodynamic Experiments and Semi empirical Predictions, echnical report, Defense R&D Canada, Ottawa, 003. 1 erziger J H, Peric M, computational Method for luid Dynamics, (Springer. verlag Berlin Heidelberg NewYork), 00, pp. 43. 13 Roddy, R., Investigation of the stability and control characteristics of several configurations of the DARPA SUBO model (DRC Model 5470) from captive-model experiments. echnical report, David aylor research center, 1990, 116. 14 SHI X, CHEN X and AN J., Study of Resistance Performance of essels with Notches by Experimental and Computational luid Dynamics Calculation Methods, J. Shanghai Jiaotong Univ., 15(010) 340-345. 15 Prestero, erification of a Six- Degree of reedom Simulation Model for the REMUS Autonomous Underwater ehicle, Massachusetts institute of technology, 001.